The present invention relates to the field of petroleum service and supply industries, and in particular to methods of controlling drilling fluids.
When drilling a well such as an oil well, a drilling fluid or mud is injected mainly for the purposes of conveying cuttings from the bottom to the surface, of cooling and lubricating the drill bit, of maintaining hole size by preventing wall narrowing or caving phenomena, and of preventing in-flow of water, oil, or gas, with the hydrostatic pressure of the drilling mud counterbalancing the pressure exerted by the fluids or gases in the formations.
Drilling mud comprises a liquid phase (water, brine, oil, water-in-oil or oil-in-water emulsion) together with solids in suspension. A wide range of materials are used, but very generally a drilling mud contains a Bentonite type clay which increase the viscosity of the mud and thus gives it good suspensive capacity to oppose any settling of the cuttings, and a weighting material, generally barium sulfate known as barite.
The drilling mud is continuously recycled by solid-separation equipment which removes the cuttings and recovers the more expensive solids, in particular the weighting materials. By way of example, the solid-separation equipment may comprise vibrators, hydrocyclones, settling basins, and centrifuges. The mud also flows through a buffer tank (xe2x80x9cactive pitxe2x80x9d) and, of course, through the well.
Properly speaking, the mud does not flow round a xe2x80x9cclosedxe2x80x9d circuit since xe2x80x9cfreshxe2x80x9d mud needs to be added as the hole becomes longer. Also, a portion of the liquid phase is entrained with the separated-out solids or is xe2x80x9clostxe2x80x9d into the well, e.g. where the well passes through formations that are very permeable. All of these losses need to be compensated by fresh mud.
In addition, the separating power of the solid control equipment is never completely effective; in other words none of the devices is capable of eliminating 100% of particles having a diameter greater than a reference diameter and 0% of particles of diameter smaller than the reference diameter. Finally, it should be observed that the flow rate of the mud in circulation may be greater than the processing capacity of the equipment.
For these various reasons, a large portion of the solids is not properly separated out. Since, on each new cycle, the larger cuttings are ground up by the drilling tool, the mud becomes richer over time in fine particles. Unfortunately, above a certain quantity of fines, it becomes necessary to reduce the speed of penetration into the formation, thereby correspondingly delaying the development of the well. Consequently, a mud that is too xe2x80x9coldxe2x80x9d must be dumped and replaced. This constitutes a significant financial loss for the well-borer.
To minimize inputs, and in particular to avoid dumping as much as possible, it is necessary to improve the overall effectiveness of solid-separation equipment, e.g. by increasing the number of vibrators or centrifuges, or by changing the circuit taken by the 20 mud, in particular by causing it to pass several times through a given device, or indeed by altering the disposition of the various devices (connecting them in series or in parallel).
The problem thus lies in finding a good compromise between the cost of tying up solid-separation equipment (and the cost of taking it to the drilling site), the cost of xe2x80x9cfreshxe2x80x9d mud, and the cost of dumping, particularly when the mud contains environmentally-harmful additives which make it necessary to perform decontamination treatment.
As a result, the industry has for several years been aware of the need for simulation tools enabling it, in particular, to predict such costs and optimize the mud circulation plan and the choice of solid-separation devices.
Initially, models were developed based on a global approach that took into consideration an initial state (an initial volume of mud having a known composition; said volume corresponding to the volume of mud present in the pit and, where appropriate, the volume in the hole as drilled so far), and the final state corresponding to a mud having a solid matter content complying with precise specifications of the well borer (density and fines content, in particular) and having a volume corresponding to that of the well once it has been drilled. In that global approach, the solid-separation system is represented merely by two coefficients: the liquid/solid ratio Y in the xe2x80x9csolidxe2x80x9d effluent and the separation efficiency E defined as the ratio of the quantity of cuttings recovered by the various solid-separation devices over the quantity of cuttings actually generated during drilling (which amounts to the inside volume of the well).
Also, as shown in accompanying FIG. 1, by assuming that the mud that is dumped has the same composition as the initial mud, that the solid-separation devices do not separate the Bentonite from the barite, and that the various phases do not interact with one another, it is possible to estimate the volumes and thus the relative costs of the mud to be added and the mud to be dumped merely by writing the various equations for conservation of mass that can be derived directly from the model.
The first advantage of the global approach is its great simplicity. Unfortunately, that simplicity is acquired by treating the mud circuit as a system under steady conditions, and that is very far from being the case. In particular, this approach takes no account of the fact that the mud circulates around a loop and that global separation efficiency depends in particular on the grain size distribution of the solid particles, which distribution varies, as mentioned above, as the mud ages, and also depends on numerous parameters such as, for example, the speed of penetration into the formation by the drill bit, the type of drilling head, the nature of the geological formations being drilled, etc.
Also, by definition, the global approach cannot model different dispositions since it assumes that the global separation efficiency of the system is known, and that is true only insofar as all of the devices are already in operation. Furthermore, the global approach cannot be used to control proper performance of the process on the basis of measurements performed on the surface, such as the density or the volume of mud in the pit.
The object of the present invention is to provide a new model for the circulation of drilling mud based on commonly accepted physical models including digital processing by time sequences as a function of parameters that may vary from one sequence to another. According to the invention, the grain size distribution of the various solids is calculated for each time sequence starting from an initial state and from the characteristics of each of the solid-separation units.
The mud circuit is modelled by a network of logic units, each of which performs an elementary action: dividing or adding flows, separating-out solids, grinding solids, and adding a flow to a volume that is being drained. Solid separation is performed in application of a partition function. The logic units are associated to model the various solid separation devices, the pit, and the well.
The elementary units process mud objects defined as being associations of n solids and p liquids, each component being characterized by its volume fraction, its density, and for the solid components, a particle size distribution. For each solid, the particle size distribution is modelled by a normalized frequency function F of the type:                               M                      a            ,            b                          =                              ∫            a            b                    ⁢                                    F              ⁡                              (                x                )                                      ⁢                          xe2x80x83                        ⁢                          ⅆ              x                                                          Equation        ⁢                  xe2x80x83                ⁢        1            
where Ma,b is the mass percentage of particles of diameter lying in the range a to b. The value of F is defined by a logarithmic curve defined by the median particle size value d50 (50% of the particles are smaller than d50) and a standard deviation coefficient "sgr" ("sgr"=d50/d16). The frequency distribution of a particle of size x is thus equal to:                               f          ⁡                      (            x            )                          =                              1                          x              ⁢                                                2                  ⁢                  πlnσ                                                              ⁢                      exp            ⁡                          (                              -                                                                            (                                                                        ln                          ⁢                                                      xe2x80x83                                                    ⁢                          x                                                -                                                  ln                          ⁢                                                      xe2x80x83                                                    ⁢                                                      d                            50                                                                                              )                                        2                                                        2                    ⁢                                          ln                      2                                        ⁢                    σ                                                              )                                                          Equation        ⁢                  xe2x80x83                ⁢        2            
The partition function G of the elementary separation units is defined in the same manner as being the primitive of a normal distribution, Gi(x)dx being the mass percentage in the xe2x80x9csolidxe2x80x9d effluent of particles of species i of size lying in the range x to x+dx. As for the frequency function F, the partition function G is characterized by a median value d50 (50% by mass of the particles of size greater than d50 are separated) and by a standard deviation coefficient.
A particularly advantageous aspect of the model of the invention is that it makes it possible, at a given moment, to calculate the efficiency of separation in any solid-separation device that is included in the mud circuit. Conversely, starting from measurements made on site of the efficiency of at least two separation devices, it is possible to invert the model and estimate the initial grain size distribution of the cuttings. It should be observed that the accuracy of this estimate is improved if two devices of different types are selected. This point is particularly advantageous since the grain size distribution of the cuttings is generally not known on a given site since it can be measured only by means of relatively sophisticated measurement devices that are more laboratory equipment than drilling platform equipment.
Other advantageous characteristics and details of the invention appear from the following description given with reference to the accompanying drawings, in which: